%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:06:52 PM UTC 2026
% Result : Theorem 2.67s 1.28s
% Output : CNFRefutation 2.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 68 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 50 ( 23 ~; 18 |; 0 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 38 ( 0 sgn 36 !; 2 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
( and_1
<=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+0.ax',and_1) ).
fof(f40,axiom,
and_1,
file('/export/starexec/sandbox/benchmark/Axioms/LCL006+2.ax',hilbert_and_1) ).
fof(f50,axiom,
( necessitation
<=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',necessitation) ).
fof(f64,axiom,
( axiom_m2
<=> ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+0.ax',axiom_m2) ).
fof(f75,axiom,
( op_strict_implies
=> ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+1.ax',op_strict_implies) ).
fof(f78,axiom,
necessitation,
file('/export/starexec/sandbox/benchmark/Axioms/LCL007+3.ax',km4b_necessitation) ).
fof(f86,axiom,
op_strict_implies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_op_strict_implies) ).
fof(f89,conjecture,
axiom_m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_0_axiom_m2) ).
fof(f90,negated_conjecture,
~ axiom_m2,
inference(negated_conjecture,[status(cth)],[f89]) ).
fof(f91,plain,
~ axiom_m2,
inference(flattening,[],[f90]) ).
fof(f92,plain,
( ! [X0,X1] : is_a_theorem(strict_implies(and(X0,X1),X0))
=> axiom_m2 ),
inference(unused_predicate_definition_removal,[],[f64]) ).
fof(f97,plain,
( necessitation
=> ! [X0] :
( is_a_theorem(X0)
=> is_a_theorem(necessarily(X0)) ) ),
inference(unused_predicate_definition_removal,[],[f50]) ).
fof(f106,plain,
( and_1
=> ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f124,plain,
( ~ and_1
| ! [X0,X1] : is_a_theorem(implies(and(X0,X1),X0)) ),
inference(ennf_transformation,[],[f106]) ).
fof(f136,plain,
( ~ necessitation
| ! [X0] :
( ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ) ),
inference(ennf_transformation,[],[f97]) ).
fof(f141,plain,
( ? [X0,X1] : ~ is_a_theorem(strict_implies(and(X0,X1),X0))
| axiom_m2 ),
inference(ennf_transformation,[],[f92]) ).
fof(f143,plain,
( ~ op_strict_implies
| ! [X0,X1] : strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f145,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| axiom_m2 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f141]) ).
fof(f152,plain,
! [X0,X1] :
( ~ and_1
| is_a_theorem(implies(and(X0,X1),X0)) ),
inference(cnf_transformation,[],[f124]) ).
fof(f172,plain,
and_1,
inference(cnf_transformation,[],[f40]) ).
fof(f182,plain,
! [X0] :
( ~ necessitation
| ~ is_a_theorem(X0)
| is_a_theorem(necessarily(X0)) ),
inference(cnf_transformation,[],[f136]) ).
fof(f187,plain,
( ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0))
| axiom_m2 ),
inference(cnf_transformation,[],[f145]) ).
fof(f189,plain,
! [X0,X1] :
( ~ op_strict_implies
| strict_implies(X0,X1) = necessarily(implies(X0,X1)) ),
inference(cnf_transformation,[],[f143]) ).
fof(f192,plain,
necessitation,
inference(cnf_transformation,[],[f78]) ).
fof(f199,plain,
op_strict_implies,
inference(cnf_transformation,[],[f86]) ).
fof(f202,plain,
~ axiom_m2,
inference(cnf_transformation,[],[f91]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(implies(and(X0,X1),X0))
| ~ and_1 ),
inference(cnf_transformation,[],[f152]) ).
tcf(c_75,plain,
and_1,
inference(cnf_transformation,[],[f172]) ).
tcf(c_85,plain,
! [X0: $i] :
( is_a_theorem(necessarily(X0))
| ~ necessitation
| ~ is_a_theorem(X0) ),
inference(cnf_transformation,[],[f182]) ).
tcf(c_90,plain,
( axiom_m2
| ~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)) ),
inference(cnf_transformation,[],[f187]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( ( necessarily(implies(X0,X1)) = strict_implies(X0,X1) )
| ~ op_strict_implies ),
inference(cnf_transformation,[],[f189]) ).
tcf(c_95,plain,
necessitation,
inference(cnf_transformation,[],[f192]) ).
tcf(c_102,plain,
op_strict_implies,
inference(cnf_transformation,[],[f199]) ).
tcf(c_105,negated_conjecture,
~ axiom_m2,
inference(cnf_transformation,[],[f202]) ).
tcf(c_134,plain,
~ is_a_theorem(strict_implies(and(sK0,sK1),sK0)),
inference(global_subsumption_just,[status(thm)],[c_90,c_105,c_90]) ).
tcf(c_139,plain,
! [X0: $i] :
( is_a_theorem(necessarily(X0))
| ~ is_a_theorem(X0) ),
inference(global_subsumption_just,[status(thm)],[c_85,c_95,c_85]) ).
tcf(c_150,plain,
! [X0: $i,X1: $i] : is_a_theorem(implies(and(X0,X1),X0)),
inference(global_subsumption_just,[status(thm)],[c_55,c_75,c_55]) ).
tcf(c_169,plain,
! [X0: $i,X1: $i] : necessarily(implies(X0,X1)) = strict_implies(X0,X1),
inference(global_subsumption_just,[status(thm)],[c_92,c_102,c_92]) ).
tcf(c_673,plain,
! [X0: $i,X1: $i] :
( is_a_theorem(strict_implies(X0,X1))
| ~ is_a_theorem(implies(X0,X1)) ),
inference(superposition,[status(thm)],[c_169,c_139]) ).
tcf(c_725,plain,
! [X0: $i,X1: $i] : is_a_theorem(strict_implies(and(X0,X1),X0)),
inference(superposition,[status(thm)],[c_150,c_673]) ).
tcf(c_742,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_134,c_725]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL542+1 : TPTP v9.3.1. Bugfixed v9.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n010.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 23:41:42 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.67/1.28 % SZS status Started for theBenchmark.p
% 2.67/1.28 % SZS status Theorem for theBenchmark.p
% 2.67/1.28
% 2.67/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.67/1.28
% 2.67/1.28 % ------ iProver source info
% 2.67/1.28
% 2.67/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 2.67/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.67/1.28 % git: non_committed_changes: false
% 2.67/1.28
% 2.67/1.28 % ------ Parsing...
% 2.67/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.67/1.28
% 2.67/1.28 % ------ Preprocessing... sup_sim: 3 sf_s rm: 28 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.67/1.28
% 2.67/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.67/1.28
% 2.67/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.67/1.28 % ------ Proving...
% 2.67/1.28 % ------ Problem Properties
% 2.67/1.28
% 2.67/1.28 %
% 2.67/1.28 % clauses 27
% 2.67/1.28 % conjectures 0
% 2.67/1.28 % EPR 0
% 2.67/1.28 % Horn 27
% 2.67/1.28 % unary 24
% 2.67/1.28 % binary 2
% 2.67/1.28 % lits 31
% 2.67/1.28 % lits eq 7
% 2.67/1.28 % fd_pure 0
% 2.67/1.28 % fd_pseudo 0
% 2.67/1.28 % fd_cond 0
% 2.67/1.28 % fd_pseudo_cond 1
% 2.67/1.28 % AC symbols 0
% 2.67/1.28
% 2.67/1.28 % ------ Schedule dynamic 5 is on
% 2.67/1.28
% 2.67/1.28 % ------ no conjectures: strip conj schedule
% 2.67/1.28
% 2.67/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.67/1.28
% 2.67/1.28
% 2.67/1.28 % ------
% 2.67/1.28 % Current options:
% 2.67/1.28 % ------
% 2.67/1.28
% 2.67/1.28
% 2.67/1.28 %
% 2.67/1.28
% 2.67/1.28 % ------ Proving...
% 2.67/1.28 %
% 2.67/1.28
% 2.67/1.28 % SZS status Theorem for theBenchmark.p
% 2.67/1.28
% 2.67/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.67/1.28
% 2.67/1.28
%------------------------------------------------------------------------------